Public transport systems in particular operations of buses, are considered as a complex system having dependencies, for example headways among busses and a number of entities, i.e. said busses that evolve over time. An enforcement of a policy, i.e. an increase or decrease of the dwell time of a bus at one bus station, which may be also termed degree of freedom, ‘DOF’, has unknown effects to the system in general due to the dependencies among the busses. These effects can for example be estimated by a simplistic model or by simulations of more complicated models considering also more detailed parameters like weather conditions, traffic, etc. In both cases, i.e. estimating the effect by a simplistic model or performed complex simulations of complicated models, every time that a measure is applied to the busses, i.e. an increase of the dwell time of a bus at one bus stop, a computation with computational cost C is required for estimation of this effect to the overall system.
The fleet of busses may have certain so-called degrees of freedom, ‘DOF’, wherein the number of said DOF is denoted with Nf. In other words Nf represents a set of policies that can be applied by an operator, for example either increase or decrease the dwell time of a bus by 1, 2, 3, 4 or more minutes at a bus station in order to achieve a global optimization on the bus system. For example since excess dwell times like ten minutes or above are usually be impractical for the bus operator and annoying to waiting passengers, other measures such as speed control, like enforcement of a reduction of an average speed of a bus between two stations, can be applied to compensate for possible limitations on the time that a bus can wait at a station.
The dwell time can also be negative if the average speed of the bus is increased after corresponding information from the bus operator. Thus, the bus operator has increased capabilities when the number of degrees of freedom Nf is higher. The bus operator is now faced with the problem of optimizing bus scheduling among all busses using measures that optimize globally the performance of the bus operation.
One possibility is a brute-force computation of the influence of each degree of freedom to the bus system leading to the following number of computations with base computational cost C:NfNE+NS, where NS is the number of stations, NE the number of buses and Nf the degree of freedom measures available to the bus operator. The computational cost of calculating a global optimum of the system grows exponentially with the number of buses and stations, hence the system has the problem that it fails to scale up in its early phase already as it is shown in FIG. 1.
In the non-patent literature of SUN Chuanjiao, ZHOU Wei, WANG Yuanqing, 2008, “Scheduling Combination and Headway Optimization of Bus Rapid Transit”, JOURNAL OF TRANSPORTATION SYSTEMS ENGINEERING AND INFORMATION TECHNOLOGY, Volume 8, Issue 5, October 2008 as well as in CN 102737356A or CN 103440422A conventional methods and systems for bus scheduling are shown.
For example CN 103440422A discloses a bus behind-schedule recovering method based on arrival time prediction with a time window. The method comprising the steps of predicating arrival time of the bus by using Kalman filtering, taking a predication result as the basis, giving out a dispatching time/judging time window, providing the behind-schedule recovering concept introducing a time deviation coefficient as well as taking a corresponding speed of a critical time deviation coefficient and maximum allowable speed as restrictions to establish a behind-schedule recovering model, so as to provide a speed of road segment driving to a bus driver and a dispatching center to avoid possible behind-schedule or recover a novel operation as soon as possible.